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Maths History

Algebra tiles through history

Connect modern classroom tiles with old ideas of area and unknowns.

Quick answer

Algebra tiles are a way to represent and solve algebra problems using physical or drawn shapes that show unknowns and values. They come from ancient ideas of using shapes to understand unknown amounts, and they help children learn algebra more easily by making abstract ideas more concrete.

Learning outcome

By the end of this page, you will understand how algebra tiles help you solve problems with unknowns, and you will be able to use simple algebra tiles to show and solve basic equations. Success signs:
  • You can draw or use shapes to show what an unknown number looks like
  • You can match a problem with the right tiles
  • You can solve simple equations using tiles
  • You can explain how tiles help you think about algebra

Why this matters

Algebra tiles help you understand algebra in a fun and visual way. Instead of just seeing numbers and letters, you can use shapes that look like blocks or areas. This makes it easier to think about problems with unknowns. You’ll use this idea when you solve puzzles, build things, or even play games where you need to figure out how many of something you have or need.

How it works

Algebra tiles are small shapes that represent numbers and unknowns:
  • A small square tile shows the number 1
  • A long rectangle tile shows the unknown number, often called "x"
  • A large square tile shows the unknown number times itself, or "x squared"
To solve a problem:
  1. Draw or use tiles to show what you know
  2. Use the tiles to balance both sides of the equation
  3. Find out what the unknown tile stands for

Examples you can see

Let’s imagine you have a problem like this: x + 3 = 7 Here’s how you can solve it with algebra tiles:
  1. Use a long tile for x (this is your unknown)
  2. Use 3 small square tiles for the number 3
  3. On the other side of the equals sign, use 7 small square tiles
  4. Now, take away 3 small tiles from both sides
  5. Now you have x = 4
This shows that x is 4. You can see it clearly because you took away the same amount from both sides. Another example: 2x + 1 = 5
  1. Use 2 long tiles for 2x
  2. Use 1 small tile for the number 1
  3. On the other side, use 5 small tiles
  4. Take away 1 tile from both sides
  5. Now you have 2x = 4
  6. Split the 4 tiles in half to find out what one x tile is
  7. So x = 2

Try it as a mini adventure

Imagine you are a detective solving a mystery! You find a treasure map that says: "If I add 3 apples to my bag and then find 2 more, I will have 7 apples in total." Can you figure out how many apples you had at first? Use algebra tiles to solve this:
  1. Draw a long tile for the apples you had (this is your x)
  2. Add 3 small tiles for the apples you added
  3. Draw 7 small tiles on the other side
  4. Take away 3 small tiles from both sides
  5. Now you see that x = 4
So, you had 4 apples at first!

Common mistakes

  • Mistake: Thinking that x can be any number, not just one specific value.
    Why it happens: Not understanding that x is a specific number in a problem.
    Fix: Always check if there is one correct answer for x.
  • Mistake: Adding or removing tiles from only one side of the equation.
    Why it happens: Not remembering that both sides must stay equal.
    Fix: Whatever you do to one side, you must do to the other side.
  • Mistake: Confusing the small tile (1) with the long tile (x).
    Why it happens: Not remembering what each tile stands for.
    Fix: Label each tile clearly or draw a key to help you remember.

Parent and carer guide

To help your child learn with algebra tiles:
  • Start by drawing the tiles together and naming them
  • Ask questions like, "What does this tile stand for?"
  • Let them try to solve simple problems using their own tiles
  • Use real-life examples, like sharing snacks or counting toys
  • Don’t worry if they make mistakes – it's part of learning!
Here are 5 quick ways to use algebra tiles at home:
  1. Use blocks or paper squares to make tiles
  2. Write equations on paper and solve with tiles
  3. Play a game where you guess how many tiles are in a bag
  4. Use a toy box to show how many items you have
  5. Count steps or jump rope times using tiles

Practice questions

  1. What is the value of x in x + 5 = 9?
    Answer: x = 4
  2. What is the value of x in 3x = 12?
    Answer: x = 4
  3. What is the value of x in 2x + 3 = 7?
    Answer: x = 2
  4. What is the value of x in x + 1 = 6?
    Answer: x = 5
  5. What is the value of x in 4x = 16?
    Answer: x = 4

FAQ

What are algebra tiles?

Algebra tiles are shapes that help you solve math problems. They show numbers and unknowns in a way that is easy to see and understand.

Why do we use algebra tiles?

They make algebra easier to understand by using shapes instead of just numbers and letters. This helps you see how equations work.

Can I use algebra tiles for big problems?

Yes! Algebra tiles can help solve bigger problems too, especially when you are learning about equations and unknowns.

Are algebra tiles only for math class?

No! You can use them at home, in games, or even in art projects to help with counting and solving problems.

How can I make my own algebra tiles?

You can draw them on paper, use blocks or cubes, or even use items like coins or buttons to represent numbers and unknowns.